Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 278

Diagonal Crossed Products by Duals of Quasi-Quantum Groups

F. Hausser, F. Nill

Let G be a (weak) quasi-Hopf algebra. Using a two-sided G-coactionon an algebra M, we construct what we call the diagonal crossedproduct as a new associative algebra structure on M*dG, where dG is the dual of G. This construction is largely motivated by the special case M = G, for which we obtain an explicit definition of the quantum double D(G) for quasi-Hopf algebras G. Applications of our formalism include the field algebra construction of Mack and Schomerus as well as the formulation of Hopf Spin chains or lattice currentalgebras based on truncated quantum groups at roots of unity. A complete proof that D(G) is even a (weak) quasi-triangular quasi-Hopf algebra will be given in a separate paper. q-alg/9708004

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